Question: Rewrite as a simplified fraction. ${3.6\overline{82} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3682.8282...\\ 10x &= 36.8282...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3646}$ ${x = \dfrac{3646}{990}} $ ${x = \dfrac{1823}{495}} \text{or} {3 \dfrac{338}{495}}$